quick trig problem

[TeethRCool]

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cos (116)= ?

answer is -cos(64)


Don't know why but I'm having a hard time with this problem? Any help would be appreciated. Thanks!

 

[Bradsher1984]

I dont know if you remember the old Unit Circle from Algebra class, but looking it up might be a good idea. Cos measures the x distance from the origin of the circle, and cos(116) is in the upper left quadrant, which means it will be negative. Cos (116) is 64 degrees away from 2PI, or 180 degrees, if we go clockwise. Looking across the unit circle, it should be obvious that cos 64 is symmetrical with cos 116 and should have the same absolute value as cos 116.

Find a unit circle online or from an old math book and this should be a peice of cake. Hope that helps

 

[Bradsher1984]

Oh, also, make sure you know the difference between cos(-64) and -cos(64). I had to remember to keep that straight a few times.

 

[lifeisgood]

I dont know if you remember the old Unit Circle from Algebra class, but looking it up might be a good idea. Cos measures the x distance from the origin of the circle, and cos(116) is in the upper left quadrant, which means it will be negative. Cos (116) is 64 degrees away from 2PI, or 180 degrees, if we go clockwise. Looking across the unit circle, it should be obvious that cos 64 is symmetrical with cos 116 and should have the same absolute value as cos 116.

Find a unit circle online or from an old math book and this should be a peice of cake. Hope that helps

You have the right idea about using the unit circle...although I am pretty sure that 116 degrees is about 64 away from pi as you go counterclockwise. This puts the angle in quadrant II and makes it negative for cosine like Bradsher said. Remember that quadrant I = all positive, qII = sin positive, qIII = tan positive, & qIV = cos positive. Therefore if cos (116) is in qII and is negative, then cos (64) which is in qI and positive would have to be multiplied by -1 to be equivalent...

 

[Bradsher1984]

yeah, you're right, from PI

 

[wireless_doc]

Just memorize the following:
For any x,
sin(180-x) = sin(x)
cos(-x) = cos(x)
tan(180+x) = tanx
cotan(180+x) = cotan(x)

The other functions in the same form will be opposite of them. Taking the first for example,
cos(180-x) = -cos(x)
tan(180-x) = -tan(x)
cotan(180-x) = -cotan(x)

Another handy one would be sin(90-x) = cos(x); tan(90-x) = cotan(x)

If you know the unit circle, then you don't actually have to memorize.

PS: Pi is equivalent 180. If you go 2Pi (360), everything will be the same regardless which direction you go.